Probability Tools for Sequential Random Projection

• URL: http://arxiv.org/abs/2402.14026v3
• Date: Sun, 12 May 2024 05:59:46 GMT
• Title: Probability Tools for Sequential Random Projection
• Authors: Yingru Li,
• Abstract summary: We introduce the first probabilistic framework tailored for sequential random projection. The analysis is complicated by the sequential dependence and high-dimensional nature of random variables. By employing the method of mixtures within a self-normalized process, we achieve a desired non-asymptotic probability bound.
• Score: 1.6317061277457001
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce the first probabilistic framework tailored for sequential random projection, an approach rooted in the challenges of sequential decision-making under uncertainty. The analysis is complicated by the sequential dependence and high-dimensional nature of random variables, a byproduct of the adaptive mechanisms inherent in sequential decision processes. Our work features a novel construction of a stopped process, facilitating the analysis of a sequence of concentration events that are interconnected in a sequential manner. By employing the method of mixtures within a self-normalized process, derived from the stopped process, we achieve a desired non-asymptotic probability bound. This bound represents a non-trivial martingale extension of the Johnson-Lindenstrauss (JL) lemma, marking a pioneering contribution to the literature on random projection and sequential analysis.

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